On the distribution of power residues and primitive elements in some nonlinear recurring sequences

Bulletin of the London Mathematical Society

Volumn 35, Issue 4, 2003, Pages 522-528

  Niederreiter, Harald ^a   Shparlinski, Igor E ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038166139     PISSN: 00246093     EISSN: None     Source Type: Journal    
DOI: 10.1112/S002460930300198X     Document Type: Article

References (16)

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2. F. GRIFFIN, H. NIEDERREITER and I. E. SHPARLINSKI, On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders, Lecture Notes in Computer Science 1719 (Springer, Berlin, 1999) 87-93.
3. J. GUTIERREZ and D. GOMEZ-PEREZ, Iterations of multivariate polynomials and discrepancy of pseudorandom numbers, Lecture Notes in Computer Science 2227 (Springer, Berlin, 2001) 192-199.
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5. N. M. KOROBOV, 'The distribution of non-residues and of primitive roots in recurrence series', Doklady Akad. Nauk SSSR 88 (1953) 603-606 (Russian).
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9. H. NIEDERREITER and I. E. SHPARLINSKI, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Appl. Algebra Engrg. Comm. Comput. 10 (2000) 189-202.
10. H. NIEDERREITER and I. E. SHPARLINSKI, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Math. Comp. 70 (2001) 1569-1574.
11. H. NIEDERREITER and I. E. SHPARLINSKI, 'Recent advances in the theory of nonlinear pseudorandom number generators', Monte Carlo and Quasi-Monte Carlo Methods 2000 (ed. K.-T. Fang, F. J. Hickernell and H. Niederreiter, Springer, Berlin, 2002) 86-102.
12. H. NIEDERREITER and I. E. SHPARLINSKI, 'On the average distribution of inversive pseudorandom numbers', Finite Fields Appl. 8 (2002) 491-503.
13. H. NIEDERREITER and A. WINTERHOF, 'Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators', Acta Arith. 93 (2000) 387-399.
14. H. NIEDERREITER and A. WINTERHOF, 'On the distribution of compound inversive congruential pseudorandom numbers', Monatsh. Math. 132 (2001) 35-48.
15. H. NIEDERREITER and A. WINTERHOF, 'On a new class of inversive pseudorandom numbers for parallelized simulation methods', Period. Math. Hungar. 42 (2001) 77-87.
16. I. E. SHPARLINSKI, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mat. Zametki 24 (1978) 603-613 (Russian).